1. The problem is to convert the number 0111000012 from base 3 (ternary) to octal (base 8). 2. First, note that the number 0111000012 is given in base 3 because it contains digits 0, 1, and 2 only. 3. To convert from base 3 to base 8, a good approach is to first convert the base 3 number to decimal (base 10), then convert that decimal number to octal. 4. Convert 0111000012 from base 3 to decimal using the formula: $$\text{Decimal} = \sum_{i=0}^{n-1} d_i \times 3^i$$ where $d_i$ is the digit at position $i$ from right to left (starting at 0). 5. Write the digits with their powers: $$0 \times 3^9 + 1 \times 3^8 + 1 \times 3^7 + 1 \times 3^6 + 0 \times 3^5 + 0 \times 3^4 + 0 \times 3^3 + 0 \times 3^2 + 1 \times 3^1 + 2 \times 3^0$$ 6. Calculate each term: $$0 + 1 \times 6561 + 1 \times 2187 + 1 \times 729 + 0 + 0 + 0 + 0 + 1 \times 3 + 2 \times 1$$ $$= 0 + 6561 + 2187 + 729 + 0 + 0 + 0 + 0 + 3 + 2$$ 7. Sum all terms: $$6561 + 2187 + 729 + 3 + 2 = 9482$$ 8. Now convert decimal 9482 to octal by dividing by 8 repeatedly and recording remainders: - $9482 \div 8 = 1185$ remainder $2$ - $1185 \div 8 = 148$ remainder $1$ - $148 \div 8 = 18$ remainder $4$ - $18 \div 8 = 2$ remainder $2$ - $2 \div 8 = 0$ remainder $2$ 9. Write the octal digits from last remainder to first: $22412$ 10. Therefore, the octal equivalent of 0111000012 (base 3) is $22412$ (base 8).